Inequality and Network Structure
Columbia University - Department of Industrial Engineering and Operations Research (IEOR)
Northwestern University; Tilburg University - CentER for Economic Research
Columbia University, Barnard College - Department of Economics; Santa Fe Institute
Santa Fe Institute; University of Massachusetts
August 6, 2008
CentER Discussion Paper Series No. 2008-76
This paper explores the manner in which the structure of a social network constrains the level of inequality that can be sustained among its members. We assume that any distribution of value across the network must be stable with respect to coalitional deviations, and that players can form a deviating coalition only if they constitute a clique in the network. We show that if the network is bipartite, there is a unique stable payoff distribution that is maximally unequal in that it does not Lorenz dominate any other stable distribution. We obtain a complete ordering of the class of bipartite networks and show that those with larger maximum independent sets can sustain greater levels of inequality. The intuition behind this result is that networks with larger maximum independent sets are more sparse and hence offer fewer opportunities for coalitional deviations. We also demonstrate that standard centrality measures do not consistently predict inequality. We extend our framework by allowing a group of players to deviate if they are all within distance k of each other, and show that the ranking of networks by the extent of extremal inequality is not invariant in k.
Number of Pages in PDF File: 25
Keywords: inequality, networks, coalitional deviations, power, centrality
JEL Classification: C71, D30, D85working papers series
Date posted: September 16, 2008
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